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As far as I know, there is usually a betwixt in choosing the right value for a threshold. A trade off between bias and variance has to be encountered.

If a low threshold is chosen, the number of observations (exceedances) increase and the estimation becomes more smooth.

However, low threshold also introduces some observations from the center of the distribution and the estimation becomes biased.

On the other hand, a relatively high threshold eliminates values that would have been part of the extrema hence a higher variance in the estimations.

How do I know the value of a threshold chosen is fit to produce the best results? Moreover, If I am to do a trade off between , what would be worth? Overlook bias and ensure minimal variance or forsake variance and combat bias? Which is better? Are there any texts that I can refer to?

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The basic method is to plot the result against different thresholds and use the one where it starts to converge. If you use the Hill-estimator it's called Hill-plot. But a lot of variants exist in EVT.

Also see: https://www.ine.pt/revstat/pdf/rs120102.pdf

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  • $\begingroup$ Thanks so much. Yeah I know the hill estimator and the corresponding plot. But does it then mean its not possible to have a uniform threshold for the same data when two or more people are trying to study the same data set. $\endgroup$ – KaRJ XEN Sep 5 '16 at 5:55
  • $\begingroup$ Sorry, I'm not sure what you mean. Why shouldn't it be possible to use the same theshold? $\endgroup$ – Ami44 Sep 5 '16 at 18:00
  • $\begingroup$ Ok what I meant is. So when two people are working with the same data set, it is not expected that they can use the same threshold. And if they do, its just a coincidence but should not always be expected. Is that so? $\endgroup$ – KaRJ XEN Sep 6 '16 at 6:20
  • $\begingroup$ Yes, this graphical methods are subjective to a certain extent and are the most popular I guess. But if you look at the paper I referenced you will also find some automated methods. $\endgroup$ – Ami44 Sep 6 '16 at 21:02

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